While the empirical assessment of compositions of the \( G \) -block with other blocks is encouraging[1]}, [2]}, [3]}, the formal analysis of its most general case has been confined to self-stablization [4]}, and that under the assumption that all states lie in Noetherian rings and are thus a priori bounded.
Unlike global uniform asymptotic stability (GUAS) [5]}, [6]}, self-stabilization has no notion of robustness to perturbations, while perturbations are to be expected in any feedback composition.
Thus we improve the generalized \( G \) -block to allow removal of the Noetherian assumption, proof of GUAS,
and (under an additional Lipschitz condition) ultimate boundedness in face of persistent perturbations.
Finding ultimate bounds further anticipates the development of sophisticated variants of the small gain theorem [7]}, [5]} for closed loop analysis.
